Local EPR-experiments with photons in vacuum?Indeed, the line from A to B is something called a "null interval" which is totally entirely completely unrelated to the concept of "empty intervals" of real numbers in high-school math. These two things are just as unrelated as the "intervals" in music theory and in aerobics. That's why I still think you should mentally rename it a "null shminterval".

Local EPR-experiments with photons in vacuum?Indeed, I am saying that the term "null interval" in special relativity has a very very different definition than an "empty interval" in the sense of intervals of real numbers. If you don't believe me, try looking up the former definition in an SR textbook, and then looking up the latter definition in a high school math textbook. You will see that they are completely different and unrelated.

Jan9

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Local EPR-experiments with photons in vacuum?Sometimes words have multiple meanings. You found an article called "Interval (mathematics)" which has a certain definition of "Interval". But you are wrong to conclude that this is the universal and only definition of the word "Interval". The more relevant article is en.wikipedia.org/wiki/Interval , which proves that the word "Interval" has at least 15 different definitions. The word "interval" in the context of special relativity means something different than the the word "interval" in the context of the number line, just as it means something different in music, or in sports. :-D

Jan9

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Local EPR-experiments with photons in vacuum?When you say "all properties of an interval", I think you mean "all the properties that I intuitively expect an interval to have", but your intuition is wrong because your intuition is based on a lifetime of experience with Euclidean geometry. Well, you're entitled to have the opinion: Anything that deserves to be called an interval must certainly have the following properties...!. But you must understand that other people do not feel this way. That's why I suggest that you mentally replace the word "interval" with "shminterval", a made-up word which is therefore free of your preconceptions.